1. Field of the Invention
The present invention relates to a linear estimation method for a three-dimensional position with affine camera correction, and more particularly, it relates to a linear estimation method for a three-dimensional position with affine camera correction for estimating the three-dimensional position of an object point in a three-dimensional space from images acquired by a plurality of cameras in case of controlling a robot or the like with image information.
2. Description of the Prior Art
A method of acquiring an image of a point (object point) existing in a three-dimensional space with a camera and estimating its three-dimensional position is a central problem of computer vision. Stereoscopy can be referred to as the most basic technique for solving this problem. In the stereoscopy, two cameras located on previously known positions in previously known orientations acquire images of an object point, for deciding its three-dimensional position from the projected images with the principle of triangulation. In such stereoscopy, it is necessary to correctly measure the positions, orientations and focal lengths of the cameras. This is called camera calibration, which has generally been studied in the fields of computer vision and robotics. In this case, the relation by perspective projection is generally employed as the method of describing the relation between the three-dimensional space and the images.
This perspective projection model can be regarded as an ideal model for general cameras. Despite its correctness, however, this projective model is nonlinear. Due to such non-linearity, three-dimensional position estimation is weak against computation errors or measurement errors of the projected points.
Study has been made for approximating the perspective projection model with a camera model which has better properties. For example, "Geometric Camera Calibration using Systems of Linear Equations" by Gremban, Thorpe and Kanade, International Conference on Robotics and Automation, pp. 562-567 (1988) applies approximation of a camera model to camera calibration. Thereafter study of an affine camera model has been developed in "Self-Calibration of an Affine Camera from Multiple Views" by Quan, International Journal of Computer Vision, Vol. 19, No. 1, pp. 93-105 (1996). The affine camera model describes a three-dimensional space and images in linear relation. It is known that the affine camera model solves problems resulting from non-linearity and provides sufficiently good approximation of a perspective projection model if the thickness of the object is sufficiently smaller than the distance between the camera and the object.
"Euclidean Shape and Motion from Multiple Perspective Views by Affine Iterations" by Christy and Horaud, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 18, No. 11, pp. 1098-1104 (1996) describes an applied example of this affine camera model in three-dimensional position estimation. This example is adapted to approximately estimate the three-dimensional position of an object point with an affine camera model for optimizing nonlinear equations obtained from a perspective camera with the approximate value employed as an initial value thereby further correctly estimating the three-dimensional position of the object point. However, this method requires the operation of optimizing the nonlinear equations, and cannot be regarded as a simple solution.
Multiple-camera stereoscopy employing a plurality of (at least two) cameras forms another flow of the stereoscopy. In the multiple-lens stereoscopy, it is expected that the information content increases as compared with the case of employing only two cameras and the three-dimensional position can be further stably estimated. For example, "Shape and Motion from Image Streams under Orthography: a Factorization Method" by Tomasi and Kanade, International Journal of Computer Vision, Vol. 9, No. 2, pp. 137-154 (1992) describes an example of such multiple-camera stereoscopy. According to Tomasi et al., it is possible to estimate a three-dimensional position by a simple method called a factorization method, if a plurality of orthographic projection cameras can be assumed. If the cameras are not orthographic projection cameras, however, it is necessary to satisfy nonlinear constraint condition called epipolar constraint for three-dimensional position estimation. Therefore, the three-dimensional position cannot be readily estimated.